A bath toy is floating stationary in water such that half of the toy is above water and half of the toy is below the water. A kid pulls the toy 3.3 cm down into the water and then lets go. The toy then proceeds to bob up and down. It bobs up and down 18 times in a minute.

Question

A bath toy is floating stationary in water such that half of the toy is above water and half of the toy is below the water. A kid pulls the toy 3.3 cm down into the water and then lets go. The toy then proceeds to bob up and down. It bobs up and down 18 times in a minute.

NOTE: Let up be positive and down be negative for this problem

(e) Using the equation x=-3.3*cos(1.88*t), Where is the toy at time t = 7.92 second?

(f) Give meaning to your answer in part (e). Is the toy mostly above the water or below the water at this time. Explain with evidence how you know thi

Answer 1

(e) Plugging in t = 7.92 into the equation x = -3.3 * cos(1.88 * t), we get x = -3.3 * cos(1.88 * 7.92) ≈ -1.4 cm.

(f) The toy is at a position of approximately -1.4 cm at t = 7.92 seconds. This means that the toy is below the water at this time. To determine this, we look at the amplitude of the cosine function in the equation given (-3.3). Since the amplitude represents how far the toy goes above and below the water level, the fact that the toy is at -1.4 cm means it is below the water (as the water level is at 0 cm).